I've considered a number of different styles of rulership for Cumana, which Andrej would know fairly well - thinking how would half-orcs go about things, and how would an ongoing Cuman (and Pecheneg) culture manifest? I've stumbled across something which I like ... and which identify the culture as something unique.
To begin with, the ruling 'class' would be a series of clan heads, which the half-orcs call "hetmen" - a Slavic term, unfortunately, but adopted from the Germanic and therefore, I think, acceptable for the Donbass. There are approximately three hundred hetmen, each mastering between a few hundred to a few thousand clanspeople. These rarely meet, gathering together only when it is time to 'elect' a king - who is chosen upon merit, and not necessarily upon ascestral background. Occasionally, five or six hetmen will join to press a local issue; more might join to wage limited war, with or without the king's permission, against groups such as the Turks, the cossacks or the Russians. Many hetmen are paid tribute by forces outside of Cumana in order to retain their 'loyalty' to a particular foreign desire.
Although Cumana is decentralized, the vast centre of Mutrakan, consisting of both permanent and impermanent structures (a 'tent city') consists of the twenty largest tribes, more than 80,000 people ... and when aroused will tend to carry all else in its sway. Thus, the outer ring of hetmen are cautious not to arouse the central power.
The status of many of the people - particularly the youngest of the population - is that of indentured slave. It is common for families to sell their children into slavery in order to obtain wealth with which to build a flock. These children then live the first twenty to thirty years of their life as forced labor, soldiers or artisans, without choice, until such time as they have been deemed worthy of freedom - which is granted by the hetman of the tribe. Until such time, they are 'owned' by the hetman. However, during this period of ownership, the young are taught useful skills, and the brightest are given to intellectual tasks, to learn to be priests, or perhaps thieves and assassins if their owners are so inclined. Andrej, obviously, spent his years in bondage learning to be a cleric, in a tribe whose hetman had adopted Christianity.
Most Cumans are animistic in religion - neither Christian nor Muslim, viewing their time on earth as a sort of slavery before being freed by death to become ultimately free upon the 'Great Steppe,' which they call the afterlife. "All alive are slaves," is a common Cumanese saying.
Upon obtaining freedom, boys and girls are paired together and made into families - largely against their will - and are encouraged to bring forth children to sell to the hetman of their tribe. Andrej was not expected to do this - his hetman - Roggto - allowed him to pursue his wish of travelling to Europe. But should Andrej return to his home tribe, he would be asked to marry and bring forth children. Couples who do not give birth to children by their 40th year are typically cast out from the tribes, where they wander and most commonly die. This sort sees themselves has having failed their people, and believe themselves to be condemned to 'Jorghatha' ... the gray sea, where one is trapped beneath pools of thick, salt water for the rest of eternity.
I trust, Andrej, this does not seriously alter your conception of home - I hadn't needed to create a culture for Cumana before, but I quite like the ideal described above.